Abstract We first establish, through a Berry–Esseen-type bound, the asymptotic normality of a local linear estimate of the regression function in a fixed design setting when the errors are stationary isotropic spatial random fields. On the other hand, we investigate the weak convergence of an empirical estimate of the variance of these errors in a general α-mixing setting.

中文翻译：

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空间模型的趋势函数和自协方差估计

摘要 我们首先通过 Berry-Esseen 型界建立固定设计设置中回归函数局部线性估计的渐近正态性，当误差为平稳各向同性空间随机场时。另一方面，我们研究了在一般 α 混合设置中这些误差方差的经验估计的弱收敛性。